Question: Simplify the following expression: $ q = \dfrac{10r}{9r - 9} - \dfrac{-1}{6} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{6}{6}$ $ \dfrac{10r}{9r - 9} \times \dfrac{6}{6} = \dfrac{60r}{54r - 54} $ Multiply the second expression by $\dfrac{9r - 9}{9r - 9}$ $ \dfrac{-1}{6} \times \dfrac{9r - 9}{9r - 9} = \dfrac{-9r + 9}{54r - 54} $ Therefore $ q = \dfrac{60r}{54r - 54} - \dfrac{-9r + 9}{54r - 54} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{60r - (-9r + 9) }{54r - 54} $ Distribute the negative sign: $q = \dfrac{60r + 9r - 9}{54r - 54}$ $q = \dfrac{69r - 9}{54r - 54}$ Simplify the expression by dividing the numerator and denominator by 3: $q = \dfrac{23r - 3}{18r - 18}$